Device for extracting a plurality of space frequency components

ABSTRACT

A device for extracting a plurality of space frequency components from an optical image formed by an image forming optical system comprises a photoelectric element array including at least N photoelectric elements disposed in or near the image formation plane of the image forming optical system, and means for generating, on the basis of the output of each of the photoelectric elements of the array, an electrical output varying in phase in accordance with the displacement of the optical image in the direction of arrangement of the photoelectric elements.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a photoelectric conversion device, andparticularly to a device for extracting a plurality of space frequencycomponents from an optical image.

2. Description of the Prior Art

Various devices for electrically extracting information related to thespecific space frequency component of an optical image and detecting,for example, the focus of an optical system on the basis thereof havebeen proposed. We already filed, on Nov. 13, 1978, U.S. Application Ser.No. 959,918 (German counterpart P 2848874), now U.S. Pat. No. 4,218,623,covering a device for converting the outputs of the photoelectricelement of a photoelectric element array upon which an optical image isprojected into vectors having magnitudes corresponding to the magnitudesof said outputs, i.e. absolute values, and phases successively deviatedby 2π/N each (N is an integer equal to or greater than 2) in the orderof arrangement of the photoelectric elements and adding together thosevectors to thereby extract specific space frequency componentinformation having, as the space period, the length of N photoelectricelements in the direction of arrangement. However, such a specific spacefrequency component extracting device is useless when the optical imagescarcely contains the specific space frequency component, and it isimpossible to detect the focus of the optical system on the basis of theoutput of this device.

To avoid such a situation, a plurality of space frequency components maybe extracted from the optical image. For this purpose, it occurs to mindto use a plurality of photoelectric element arrays or to divide a singlephotoelectric element array into a plurality of areas and extractdiscrete space frequency components in respective ones of the arrays orareas, but this method does not enable a plurality of space frequencycomponents to be extracted from the same optical image and also suffersfrom a disadvantage that it requires a number of photoelectric elements.

SUMMARY OF THE INVENTION

It is the object of the present invention to provide a device forextracting a plurality of space frequency components in an optical imageprojected upon a photoelectric element array from the same photoelectricelement output of that array.

The device of the present invention for extracting a plurality of spacefrequency components from an optical image formed by an image formingoptical system comprises a photoelectric element array including atleast N photoelectric elements disposed in or near the image formationplane of the image forming optical system, and means for generating, onthe basis of the output of each of the photoelectric elements of thearray, an electrical output varying in phase in accordance with thedisplacement of the optical image in the direction of arrangement of thephotoelectric elements. Said means includes first vectorizing means forconverting the outputs of the photoelectric elements into vectors sothat the output of the nth photoelectric element of the array becomes avector having an absolute value related to said output and a phase givenby π/N×p₁ ×n, first adding means for adding together the vector outputsof the first vectorizing means, second vectorizing means for convertingthe outputs of the photoelectric elements into vectors so that theoutput of the nth photoelectric element of the array becomes a vectorhaving an absolute value related to said output and a phase given by2π/N×p₂ ×n, and second adding means for adding together the vectoroutputs of the second vectorizing means, where p₁ and p₂ are differentintegers less than N/2.

The invention will become more fully apparent from the followingdetailed description thereof taken in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram for illustrating the principle of the presentinvention.

FIGS. 2A-2D show vectors for illustrating the present invention.

FIGS. 3A--3F are circuit diagrams showing a first embodiment of thedevice according to the present invention.

FIGS. 4A-4H and FIGS. 5A-5D are pulse waveform illustrations showing thephase in which switching elements are controlled.

FIG. 6 is a circuit diagram showing a second embodiment of the deviceaccording to the present invention.

FIG. 7 is a circuit diagram showing a third embodiment of the deviceaccording to the present invention.

FIGS. 8A and 8B are circuit diagrams showing a fourth embodiment of thedevice according to the present invention.

FIG. 9 shows a modification of the arrangement of the photoelectricelement array included in the device of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1 which is a block diagram for illustrating theprinciple of the present invention, a photoelectric element array 1 isprovided in or near the focal plane of an image forming optical system,not shown, and this array comprises eight photoelectric elements D₁ -D₈arranged spatially in a row. Photoelectric outputs i₁ -i₈ are taken outfrom the photoelectric elements D₁ -D₈ and the values thereof representthe intensities of the lights incident on the photoelectric elements. Inthe present invention, vectorizing means 3 is further provided and thiscomprises multipliers 3_(a) -3_(h) to which the photoelectric outputsare imparted. The multipliers 3_(a) -3_(h) multiply the photoelectricoutputs i₁ ˜i₈ by vectors v₁ =exp(2π×p/8)˜v₈ =exp(2π×8p/8) so that anarbitrary photoelectric output i_(n) is multiplied by a vector v_(n)=exp(2π×np/8) (n=1˜8). Consequently, the vectorizing means converts thephotoelectric outputs i₁ ˜i₈ into vectors i₁ v₁ ˜i₈ v₈ having absolutevalues corresponding to the magnitudes thereof and phases deviated by2πp/8 each in the order of arrangement of the photoelectric elements.These vectors put out from the multipliers 3_(a) -3_(h) are applied toadding means 5. The adding means adds together the vectors i₁ v₁ ˜i.sub.8 v₈. Accordingly, the composite vector I_(p) which is the output ofthis adding means is ##EQU1## Of course, when the number of thephotoelectric elements is generalized into N, the foregoing equationbecomes ##EQU2##

This composite vector I_(p) will now be considered.

(1) When p=1, the composite vector becomes ##EQU3##

This is the sum of the outputs of the eight photoelectric elements D₁-D₈ multiplied by the vectors v₁ -v₈ out of phase by 2π/8 each as shownin FIG. 2A, and as is apparent from the above equation, it includes muchof the space frequency component having the length d of the eightelements D₁ -D₈ as the space period. In this case, one period is dividedby eight photoelectric elements, it also slightly includes theinformation of the space frequency component having d/7 as the spaceperiod and higher degrees of space frequency component. Accordingly,when p=1, the composite vector I₁ is one from which the space frequencycomponent of space period d in the light image projected upon the array1 has been chiefly extracted.

(2) When p=2, the composite vector I₂ is ##EQU4## This is the sum of theoutputs of the elements D₁ -D₈ multiplied by the vectors v₁ -v₈successively out of phase by π/2 each as shown in FIG. 2B, and it is avector from which the space frequency component of space period d/2 inthe light image has been chiefly extracted.

(3) When p=3 and p=4, the composite vectors I₃ and I₄ respectively arethe sum of the photoelectric outputs i₁ -i₈ multiplied by the vectors v₁-v₈ out of phase by 3π/4 and π as shown in FIGS. 2C and 2D, and they arevectors from which the space frequency components of space periods d/3and d/4, respectively, have been chiefly extracted.

In the foregoing, the composite vectors I₁ -I₃ include the magnitudes ofthe respective spacific space frequency components and phaseinformation, whereas the composite vector I₄ as the output includes onlymagnitude information and does not include phase information, as isapparent from FIG. 2D.

When p=0, I₀ represents the total quantity of light incident on thephotoelectric elements D₁ -D₈.

Accordingly, by individually providing vectorising means and addingmeans for p=1, p=2, p=3 and p=4, the information of space frequencycomponents of space periods d, d/2, d/3 and d/4 can be extracted.

The value which p can assume is an integer equal to or less thanone-half of the number N of the photoelectric elements constituting themaximum space period of a plurality of space frequency components whichit is desired to extract, namely, N/2. Accordingly, the value which pcan assume in the foregoing example is substantially 1 to 4 and if passumes 5 or a greater value, the extracted information becomesidentical to any of the cases where p=1˜p=4 and after all, results inany of p=1˜p=4. For example, the information extracted when p=5 isidentical to p=3.

Embodiments of the present invention will now be described. FIG. 3Ashows an embodiment of the photoelectric converting unit of the deviceaccording to the present invention. A photodiode array 1 comprises eightparallel-connected photodiodes D₁ -D₈. FET switching elements S₁ -S₈ areconnected to the respective photodiodes, thereby forming a firstswitching element group 6. The FET switching elements S₁ -S₈ are allmade to have the same period by a pulse generator 7, but the FETswitching elements S₁ to S₈ are successively momemtarily switched onwith a predetermined time delay. Accordingly, the photodiodes D₁ -D₈generate photoelectric outputs related to said period and theintensities of incident light upon switching-on of the associated FETswitching elements S₁ -S₈.

The photoelectric outputs are imparted to a sampling hold circuit 9.This sampling hold circuit 9 comprises an operational amplifier 9a, afeedback capacitor 9b and a reset switch 9c. The sampling hold circuit 9temporally holds the photoelectric outputs successively generated by thephotodiodes D₁ -D₈ at a predetermined time interval upon switching-on ofthe the FET switching elements S₁ -S₈. The reset switch 9c ismomemtarily switched on immediately before the switching-on of each FETswitching element S₁ -S₈ to reset the previously held photoelectricoutput for the purpose of holding the next photoelectric output.

The output of the sampling hold circuit 9 is applied to a secondswitching element group 11. This second switching element group 11comprises parallel-connected FET switching elements S₁₁ -S₁₈, which aresuccessively switched on with a predetermined time delay by the pulsegenerator 7 in synchronism with the FET switching elements S₁ -S₈. Inthis manner, the FET switching element S₁₁ delivers the photoelectricoutput of the photodiode D₁ held by the sampling hold circuit 9 to ahold circuit 13a comprising a capacitor and an operational amplifier,the FET switching element S₁₂ delivers the similar photoelectric outputof the photodiode D₂ to a hold circuit 13b, and likewise the FETswitching elements S₁₃ -S₁₈ deliver the photoelectric outputs of thephotodiodes D₃ -D₈ to hold circuits 13c-13h, respectively. Thus, thephotoelectric outputs of the photodiodes D₁ -D₈ are time-sequentiallytaken out and successively held by the corresponding hold circuits13a-13h. The photoelectric outputs put out at the output terminals T₁-T₈ of these hold circuits 13a-13h are defined as i₁ -i₈ correspondingto the photoelectric outputs i₁ -i₈ of FIG. 1.

A circuit for extracting the space frequency component of space period dfrom the photoelectric outputs i₁ -i₈ will now be described withreference to FIG. 3B. Terminals T_(1a) -T_(8a) are connected tocorresponding output terminals T₁ -T₈ in such a manner that, forexample, T_(1a) is connected to T₁. These terminals T_(1a) -T_(8a)provide the input terminals of a vectorizing circuit 30A. Thevectorizing circuit 30A comprises resistors R connected to the outputterminals and a third switching element group S₂₁ -S₂₈ series-connectedto each of the resistor R. The switching elements S₂₁ -S₂₈ are allswitched on and off at the same period T, as shown in FIGS. 4A-4H. Thetime during which these switching elements are switched on and the timeduring which these switching elements are switched off are equal to eachother. Each of the switching elements S₂₁ -S₂₈ has a time delay of T/8,i.e. 2π/8. Accordingly, the photoelectric outputs i₁ -i₈ aresuccessively imparted a phase delayed by T/8, i.e. 2π/8 in the order ofarrangement of the elements by the switching elements S₂₁ - S₂₈, and areconverted into rectangular wave AC signals or vectors having amplitudesrelated to the magnitudes of the photoelectric outputs and said phase.These AC signals are added together by a common conductor 50A which actsas adding means 5.

The vector signals added together are applied to a band-pass filter 19Ahaving a pass band in an angular frequency 2π/T. This filter extractsonly the sine wave component of angular frequency 2π/T from therectangular wave AC signals.

What has been described above will now be expressed by mathematicalexpressions. After the photoelectric outputs i₁ -i₈ have been convertedinto rectangular wave signals by the switching elements S₂₁ -S₂₈, onlythe angular frequency component of 2π/T is extracted by the band-passfilter 19A and so, in the following description, only the sine wave ofangular frequency 2π/T will be explained.

The photoelectric outputs in (n=1 . . . 8) are converted into in exp(2π/T t+2π×n/8) by the vectorizing circuit 30A. These are added togetherat a connection point 50A to provide a composite output I₁, which is##EQU5## As seen from this equation, the amplitude and phase of theoutput I₁ of the band-pass filter 19A represent the magnitude and phaseinformation of the space frequency component of space period d in thelight image.

FIG. 3C shows a circuit for extracting the space frequency component ofspace period d/2. The input terminals T_(1b) -T_(8b) of this circuit areconnected to the output terminals T₁ -T₈, respectively, in such a mannerthat the terminal T_(1b) is connected to the terminal T₁. Thephotoelectric outputs i₁ and i₅ are converted into vectors of the samephase by a vectorizing circuit 30B and are therefore applied to the sameswitching element S₃₁ through resistors R. The sets of photoelectricoutputs i₂, i₆, i₃, i₇ ; i₄, i₈ are likewise applied to the sameswitching elements S₃₂, S₃₃ and S₃₄. The switching elements S₃₁ -S₃₄have the same period T as shown in FIGS. 5A-5D, but are successivelyswitched on with a delay of T/4. The outputs of the vectorizing circuit30B are added together by a common conductor 50B which acts as an adder.The added outputs are filtered by a bandpass filter 19B. The filter 19Bmay be identical to the filter 19A. By the same reason as set forthabove, the output I₂ of the band-pass filter 19B represents theinformation of the space frequency component of space period d/2.

FIG. 3D shows a circuit for extracting the space frequency component ofspace period d/3. The input terminals T_(1c) -T_(8c) of this circuit areconnected to the output terminals T₁ -T₈, respectively, in such a mannerthat the terminal T_(1c) is connected to the terminal T₁. Switchingelements S₄₁ -S₄₈ are controlled just in the same manner as theaforementioned switching elements S₂₁ -S₂₈. The output I₃ of a band-passfilter 19c which has been subjected to addition and filtrationrepresents the information of the space frequency component of spaceperiod d/3.

FIG. 3E shows a circuit for extracting the information of the spacefrequency component of space period d/2. The input terminals T_(1d)-T_(8d) of this circuit are connected to the output terminals T₁ -T₈,respectively. As is apparent from FIG. 2D, the photoelectric outputs i₁and i₂, i₃ and i₄, i₅ and i₆, i₇ and i₈ are multiplied by vectorsdeviated by π each in phase and therefore, after all, the differencebetween the two may be taken. Therefore, the photoelectric outputs i₁,i₃, i₅ and i₇ are added together by the resistor R and the photoelectricoutputs i₂, i₄, i₆ and i₈ are likewise added together and the differencebetween the addition outputs is obtained by a differential amplifier 30to thereby obtain a composite vector I₄.

FIG. 3F shows a circuit for obtaining the total quantity of light. Theinput terminals T_(1e) -T_(8e) of this circuit are connected to theoutput terminals T₁ -T₈, respectively. The photoelectric outputs i₁ -i₈are intactly added together by an adding circuit 15 through addingresistors.

In FIG. 3C, to effectively utilize the photoelectric outputs from thearray, the information of the space frequency component of space periodd/2 has been obtained by the use of all the photoelectric outputs i₁-i₈, but this space period is equal to the length of four continuousphotoelectric elements and therefore, the information can be likewiseobtained by using only the photoelectric outputs of four continuousphotoelectric elements such as, for example, photoelectric outputs i₁-i₄ or i₅ -i₈. Of course, this also holds true with the output I₄ andthe information can be obtained from only the outputs of severaladjacent photoelectric elements.

FIG. 6 shows a second embodiment of the present invention. A logarithmicconvertion circuit group 21 connected to photodiodes D₁ -D₈ constitutinga photodiode array generates at output terminals T₁₀ -T₈₀ photoelectricoutputs proportional to the logarithm of the intensities of lightincident on the photodiodes D₁ -D₈. Terminals T_(10a) -T_(80a) areconnected to the corresponding output terminals T₁₀ -T₈₀, respectively,in such a manner that the terminal T_(10a) is connected to the terminalT₁₀. The inputs of the terminals T_(10a) and T_(50a), T_(20a) andT_(60a), T_(30a) and T_(70a), T_(40a) and T_(80a) are connected so thatthe differences therebetween are taken by differential amplifiers23A-23D, respectively. Switching elements S₅₁ -S₅₄ connected to theoutputs of the respective differential amplifiers are similar to theaforementioned switching elements S₂₁ -S₂₈ and are successively switchedon with a phase delay of T/8, i.e. π/4, as shown in FIGS. 4A-4D. Signalspassed through the switching elements S₅₁ -S₅₄ are added together by acommon conductor 25A which acts as adding means. The added outputs areobtained through an inverting amplifier 27A and a band-pass filter 29A.As is so apparent from FIG. 2A, the differences between pairs ofphotoelectric outputs (i₁ and i₅), (i₂ and i₆), (i₃ and i₇) and (i₄ andi₈) which are respectively multiplied by pairs of vectors out of phaseby π each, (v₁ and v₅), (v₂ and v₆), (v₃ and v₇) and (v₄ and v₈) areobtained by differential amplifiers 23A, 23B, 23C and 23D and therefore,phase information can be imparted to these pairs of photoelectricoutputs by common switching elements S₅₁ -S₅₄. Accordingly, in thisembodiment, the number of switching elements S₅₁ -S₅₄ may be half thenumber of switching elements S₂₁ -S₂₈ used in the first embodiment.

The case of the output I₃ is also the same as the case of the output I₁,but as shown in FIG. 2C, vectors v₁, v₂, v₃ and v₄ are out of phase by3/4π each and therefore, switching elements S₆₁ -S₆₄ connected to theoutputs of the differential amplifiers 23A-23D may be successivelyswitched on and off with a phase delay of 3/4π as shown by S₄₁, S₄₄, S₄₇and S₄₂ in FIG. 3D.

As to the case of the output I₂, as shown in FIG. 2B, the pair ofvectors v₁ and v₅ are of the same phase and therefore, i₁ and i₅ areadded together by a resistor r. Likewise, photoelectric outputs i₃ andi₇ related to the pair of vectors v₃ and v₇ of the same phase are alsoadded together. These two pairs of vectors are out of phase by π and so,the difference between the added photoelectric outputs is obtained by adifferential amplifier 23E. Photoelectric outputs i₂, i₄, i₆ and i₈related to vectors v₂, v₄, v₆ and v₈ are subjected to the sameprocessing as that described above, to thereby obtain the output of adifferential amplifier 23F. Since the vectors v₁ and v₂ are out of phaseby π/2, the output I₂ may be obtained by making the switching on and offof the switching elements S₇₁ and S₇₂ out of phase by π/2.

The output I₄ can be obtained by the construction of FIG. 3E, as alreadydescribed.

In the second embodiment, the photoelectric outputs multiplied byvectors out of phase by π have the differences therebetween calculatedin advance by the differential amplifiers 23A-23D and this leads to anadvantage that the number of the switching elements for imparting thephases of vectors to those photoelectric outputs can be reduced to halfas compared with the first embodiment. Further, these photoelectricoutputs are amplified when the differences therebetween are calculated,and such amplification is preferable because these photoelectric outputsare of relatively small values proportional to the logarithms of theintensities of light.

FIG. 7 shows a third embodiment which uses two switching elements inaccordance with a technique similar to that of FIG. 6. In FIG. 7, inputterminals T_(10c) -T_(80c) are connected to the output terminals T₁₀-T₈₀ of photodiodes D₁ -D₈ similar to those of FIG. 6 in such a mannerthat the terminal T_(10c) is connected to the terminal T₁₀. Referring toFIG. 2A, the direction of vectors v₁ and v₅ is defined as x-axis, andthe direction of vectors v₃ and v₇ is defined as y-axis, and vectors v₂,v₄, v₆ and v₈ are respectively decomposed into two vectors respectivelyhaving senses in the directions of the x-axis and y-axis, namely,vectors v_(2x), v_(2y), v_(4x), v_(4y), v_(6x), v_(6y), v_(8x), v_(8y).The size of each of these decomposed vectors is 1/√2 of the sizes ofvectors v₂, v₄, v₆ and v.sub. 8. As shown in FIG. 7, in order thatphotoelectric outputs i₁, i₂ and i₈ appearing at terminals t₁₀, T₂₀ andT₈₀ may be multiplied by vectors v₁, v_(2x) and v_(8x), terminalsT_(10c), T_(20c) and T_(80c) are connected to one input terminal of adifferential amplifier 30A through resistors r, √2r and √2·r of valuesinversely proportional to the sizes of the vectors v₁, v_(2x) andv_(8x), respectively, and in order that the photoelectric outputs i₅, i₄and i₆ of output terminals T₅₀, T₄₀ and T₆₀ may be multiplied by vectorsv₅, v_(4x) and v_(6x) which are out of phase by π with the vectors v₁,v_(2x) and v_(8x), terminals T_(50c), T_(40c) and T_(60c) are connectedto the other input terminal of the differential amplifier 30A throughresistors r, √2r and √2·r of values inversely proportional to the sizesof the vectors v₅, v_(4x) and v_(6x), respectively. By this, the outputof the differential amplifier 30A becomes a composite vector which isthe sum of photoelectric outputs i₁, i₂, i₄, i₅, i₆ and i₈ multiplied byvectors v₁, v_(2x), v_(4x), v₅, v_(6x) and v_(8x), respectively.Likewise, in order that photoelectric outputs i₃, i₂ and i₄ may bemultiplied by vectors v₃, v_(2y) and v_(4y), terminals T_(30c), T_(20c)and T_(40c) are connected to one input terminal of a differentialamplifier 30B through resistors r, √2r and √2·r, and in order thatphotoelectric outputs i₇, i₆ and i₈ may be multiplied by vectors v₇,v_(6y) and v_(8y), terminals T_(70c), T_(60c) and T_(80c) are connectedto the other input terminal of the differential amplifier 30B throughresistors r, √2r and √2·r. Thus, the output of the differentialamplifier 30B becomes a composite vector which is the sum ofphotoelectric outputs i₂, i₃, i₄, i₆, i₇ and i₈ multiplied by vectorsv_(2y), v₃, v_(4y), v_(6y), v₇ and v_(8y), respectively. In order that aphase difference of π/2 may be imparted to the outputs of thedifferential amplifiers 30A and 30B, switching elements S₈₁ and S₈₂ areswitched on and off with a phase deviation of T/4, i.e. π/2.

Thus, the final composite vector I₁ is obtained. The composite vector I₃can be obtained by the use of two switching elements through a similartechnique. Where each vector to multiply the photoelectric outputs isdecomposed into vectors having senses in the directions of the x-axisand y-axis and the photoelectric outputs are multiplied by suchdecomposed vectors, the decomposed vectors are out of phase with oneanother by π/2 or π and such phase deviation of π can be treated by adifferential amplifier and thus, the phase deviation of π/2 may betreated by the use of two switching elements.

In the embodiment of FIG. 7, the outputs of the differential amplifiers30A and 30B are modulated into rectangular waves having a phasedifference of π/2 by the switching elements S₈₁ and S₈₂ and then addedtogether, but multipliers may be used as such modulating means as shownin FIGS. 8A and 8B. Multipliers 100A and 100B each having an output (X₁-X₂)×(Y₁ -Y₂) for inputs X₁,X₂ and Y₁,Y₂ as shown in FIG. 8A may beconnected as shown in FIG. 8B and an input of a cos ωt may be impartedfrom an oscillator 101A to the multiplier 100A and an input of a sin ωtfrom an oscillator 101B to the multiplier 100B to thereby effectmodulation and the outputs thereof may be added together to obtain thefinal composite vectors I₁ and I₃.

While the present invention have been described with respect to theshown embodiments, these are mere examples and many other modificationsare conceivable. In the shown embodiments, vectorizing means convertsthe photoelectric outputs into AC outputs out of phase with one anotherin the order of arrangement of the elements, but the photoelectricoutputs can also be multiplied, for example, by vectors in the form of xand y components. In the present invention, the number of thephotoelectric elements constituting the maximum space period d is notlimited to 8 (eight). Further, the photoelectric element array comprisesN (eight in the above example) photoelectric elements corresponding tothe maximum space period d of a plurality of space frequency componentsto be extracted, but of course the array may comprise more than N,photoelectric elements. Such an example is shown in FIG. 9. In FIG. 9,the photoelectric element array 1 comprises sixteen photoelectricelements corresponding to two periods. The output terminals of everyeighth photoelectric element are connected together and connected tooutput terminals T₁₀₀ -T₈₀₀. These output terminals T₁₀₀ -T₈₀₀ in turnare connected to vectorizing circuits concerned with the space frequencycomponents to be extracted.

What we claim is:
 1. A device for extracting a plurality of spacesfrequency components from an optical image formed by an image formingoptical system, comprising:(a) a photoelectric element array includingat least N photoelectric elements disposed in or near the imageformation plane of said image forming optical system; and (b) means forgenerating, on the basis of the output of each of the photoelectricelements of said array, an electrical output varying in phase inaccordance with the displacement of said optical image in the directionof arrangement of said photoelectric elements, said means includingfirst vectorizing means for converting the outputs of said photoelectricelements into vectors so that the output of the nth photoelectricelement of said array becomes a vector having an absolute value relatedto said output and a phase given by π/N×p₁ ×n, first adding means foradding together the vector outputs of said first vectorizing means,second vectorizing means for converting the outputs of saidphotoelectric elements into vectors so that the output of the nthphotoelectric element of said array becomes a vector having an absolutevalue related to said output and a phase given by 2π/N×p₂ ×n, and secondadding means for adding together the vector outputs of said secondvectorizing means, where p₁ and p₂ are different integers less than N/2.2. The device according to claim 1, wherein each of said first andsecond vectorizing means includes:means for receiving as inputs theoutputs of two of said photoelectric elements converted into vectors outof phase by π with each other, of the outputs of said photoelectricelements, and calculating and putting out the difference between saidinputs.
 3. The device according to claim 1 or 2, wherein said integersp₁ and p₂ are p₁ =1 and p₂ =2.
 4. The device according to claim 1,wherein each of said first and second vectorizing means includes:(a)means for putting out the sum of the first direction components of theoutputs of said photoelectric elements; (b) means for putting out thesum of the second direction components of the outputs of saidphotoelectric elements which are out of phase by π with said firstdirection components; (c) means for calculating the difference betweenthe sum of the first direction components and the sum of the seconddirection components; (d) means for putting out the sum of the thirddirection components of the outputs of said photoelectric elements whichare out of phase by π/2 with said first direction components; (e) meansfor putting out the sum of the fourth direction components of theoutputs of said photoelectric elements which are out of phase by π withsaid third direction components; and (f) means for calculating thedifference between the sum of the third direction components and the sumof the fourth direction components.